Hydrogen, atom, quantum state molecular

The wavefunction plays a central role in quantum mechanics. For atomic systems, the wavefunction describing the electronic distribution is called an atomic orbital in other words, the aforementioned Is wavefunction of the ground state of a hydrogen atom is also called the Is orbital. For molecular systems, the corresponding wavefunctions are likewise called molecular orbitals. 

In writing this equation, we have made use of Van Vleck s pure precession hypothesis [12], in which the molecular orbital /.) is approximated by an atomic orbital with well-defined values for the quantum numbers n, l and /.. Such an orbital implies a spherically symmetric potential and its use is most appropriate when the electronic distribution is nearly spherical. Examples of this situation occur quite often in the description of Rydberg states. It is also appropriate for hydrides like OH where the molecule is essentially an oxygen atom with a small pimple, the hydrogen atom, on its side. Accepting the pure precession hypothesis allows the matrix elements of the orbital operators to be evaluated since... 

These summarize topological information about a molecule with atomic properties [39]. A molecular E-state index is expressed as a sum of atomic E-state indices, which are composed of two parts. First is the intrinsic atomic part, and second is perturbation, which depends on its neighborhood (other atoms in the structure). The intrinsic part includes information about the a- and 7r-orbitals, lone pairs, hydrogen atoms attached to heavy atoms, and the principal quantum numbers of valence electrons. The perturbation part is a sum of all other atomic parts modified by fimction, which descends with distance. 

Molecular Properties. Corresponding to its nuclear charge number, the nitrogen atom possesses seven shell electrons. One electron pair in in the ground state 1 s(K shell), and five electrons are distributed over the four orbitals with the principal quantum number 2 (L shell). Of these, one electron pair occupies the 2 s level and three unpaired electrons, respectively, a half of the remaining three levels, 2 px, 2 pv, 2 pz. The unpaired electrons can enter into electron-pair bonds with the 1 s electron of three hydrogen atoms. Thus, the three half occupied orbitals of the L shell become about fully accupied (formation of an octet of the neon type in accordance with the octet theory of Lewis-Langmuir). 

The Born-Oppenheimer approximation was developed in 1927 by the physicists Max Born (German) and J. Robert Oppenheimer (American), just one year after Schrodinger presented his quantum treatment of the hydrogen atom. This approximation method is the foundation for all of molecular quantum mechanics, so you should become familiar with it. The basic idea of the Born-Oppenheimer approximation is simple because the nuclei are so much more massive than the electrons, they can be considered fixed for many periods of electronic motion. Let s see if this is a reasonable approximation. Using H2 as a specific example, we estimate the velocity of the electrons to be roughly the same as that of an electron in the ground state (w = 1) of the hydrogen atom. From the Bohr formula, V = we calculate an electron velocity of 2.2 X 10 m sec . We... 

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